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Topological marker currents in Chern insulators

Nature Physics volume 15, pages 257–261 (2019)Cite this article

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Abstract

Topological states of matter exhibit many novel properties due to the presence of robust topological invariants such as the Chern index. These global characteristics pertain to the system as a whole and are not locally defined. However, local topological markers can distinguish between topological phases, and they can vary in space. In equilibrium, we show that the topological marker can be used to extract the critical behaviour of topological phase transitions. Out of equilibrium, we show that the topological marker spreads via a flow of currents emanating from the sample boundaries, and with a bounded maximum propagation speed. We discuss the possibilities for measuring the topological marker and its flow in experiment.

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Fig. 1: Lattice geometry and phase diagram.
Fig. 2: Scaling of the Chern marker.
Fig. 3: Non-equilibrium dynamics.
Fig. 4: Topological marker currents.

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Data availability

The data presented in Figs. 1b, 2, 3 and 4 can be reproduced from the equations in the main text.

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Acknowledgements

The authors are grateful for helpful conversations with H. Price, L. Privitera, V. Sacksteder and M. Fruchart. This research was supported by the Netherlands Organisation for Scientific Research (NWO/OCW), an ERC Synergy Grant, EPSRC grants EP/K030094/1 and EP/P009565/1, the Simons Foundation and Royal Society grant no. UF120157. M.D.C. and M.J.B. thank the Thomas Young Centre and the Centre for Non-Equilibrium Science (CNES) at King’s College London.

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Authors and Affiliations

  1. Instituut-Lorentz, Universiteit Leiden, Leiden, the Netherlands

    M. D. Caio

  2. Functional Materials Group, School of Physical Sciences, University of Kent, Canterbury, UK

    G. Möller

  3. TCM Group, Cavendish Laboratory, University of Cambridge, Cambridge, UK

    N. R. Cooper

  4. Department of Physics, King’s College London, London, UK

    M. J. Bhaseen

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  1. M. D. Caio
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M.D.C. performed the numerical simulations. All authors contributed to the analysis and writing of the manuscript.

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Correspondence to M. D. Caio.

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Caio, M.D., Möller, G., Cooper, N.R. et al. Topological marker currents in Chern insulators. Nat. Phys. 15, 257–261 (2019). https://doi.org/10.1038/s41567-018-0390-7

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